论文标题
分形图像作为数字序列I简介
Fractal Images as Number Sequences I An Introduction
论文作者
论文摘要
在本文中，我们将分形图像视为分形曲线，也就是说，在欧几里得空间中的网格上行走$ \ r^d $。我们将整数放置在网格的生成向量上，使相反的方向的数字相反。该编号系统将该网格上的曲线转换为一系列整数，与曲线的边缘相对应。相应的序列包含相同的分形结构，即曲线的大约对应于序列的结构。我们引入了一个归一化序列，该序列是曲线独特的。将网格发电机的形态转化为所有使用数字的字母上的签名排列。通过订购分形序列，我们获得了分形的百科全书。各种示例和图像丰富了文本。
In this article, we considered a fractal image as a fractal curve, that is, as a walk on a grid in Euclidean space $\R^d$. We placed integers on the generating vectors of a grid, such that opposite directions have opposite numbers. This numbering system converts a curve on that grid into a sequence of integers, corresponding with the curve's edges. The corresponding sequence contains the same fractal structure, i.e., an approximant of the curve corresponds to that of the sequence. We introduced a normalized sequence which is unique for a curve. The morphisms of the grid generators were translated into signed permutations on the alphabet of all the numbers used. By ordering the fractal sequences, we obtained an encyclopedia of fractals. A variety of examples and images enriched the text.
